Question 1.3.1 ([1]}) 

Let \(X\)  be a smooth proper curve, and \(D\subset X\)  a reduced effective divisor. Given a flat vector bundle \((E, \nabla )\)  on \(X\) , with regular singularities along \(D\) , let \((E^{\prime }, \nabla ^{\prime })\)  be the isomonodromic deformation of \((E,\nabla )\)  to an analytically general nearby curve \((X^{\prime }, D^{\prime })\) . Is \(E^{\prime }\)  semistable?

